Optimal quantum multi-parameter estimation and application to dipole- and exchange-coupled qubits

TL;DR

This paper develops a convex optimization approach for optimal multi-parameter quantum estimation under experimental constraints, demonstrated on coupled spin qubits, enabling precise parameter determination for high-fidelity quantum gate implementation.

Contribution

It introduces a general convex optimization framework for quantum multi-parameter estimation, applied to realistic qubit systems with unknown coupling parameters.

Findings

Optimal experimental strategies for estimating qubit coupling parameters.

Convex optimization effectively solves constrained quantum estimation problems.

Method applicable to various quantum systems beyond the studied example.

Abstract

We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for estimating multiple unknown parameters of a quantum process and apply this method to a realistic example. The example is two electron spin qubits coupled through the dipole and exchange interactions with unknown coupling parameters -- explicitly, the position vector relating the two qubits and the magnitude of the exchange interaction are unknown. This coupling Hamiltonian generates a unitary evolution which, when combined with arbitrary single-qubit operations, produces a universal set of quantum gates. However, the unknown parameters must be known precisely to generate high-fidelity gates. We use the Cram\'er-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters, and present a complete analysis of the optimal experimental configuration. Our method of transforming the constrained optimal parameter estimation problem into a convex optimization is powerful and widely applicable to other systems.